Table Talk Newsletter #34

Have you seen that Table Talk Math is now a book and available on Amazon? Check it out and let me know what you think!

How many pipes are stacked on the bed of the truck?

How did you count?

On our way to baseball practice last week, my family and I were approaching the back of a shipping truck carrying a whole bunch of steel pipes. From the back, my 6 year-old belted out, "wow, that's a lot of pipes!"

It sure was! Where were they heading? What could they be used for? How much is all that steel worth? While those questions ran through my mind, two others were more accessible: how many do you see, and how did you count?

My youngest, 4 years young, went with his upper bound: "A ZILLION!"

My oldest, the 6 year-old, started counting. Well, I wasn't about to sit behind this truck for two hours, so I had him count as much as he could and then guess. He has not yet learned multiplication, so his counting to 27 and guess of 500 was just that: a guess.

Meanwhile, my wife and I took a swing at the number. Here's what I did:

In the bottom left, there is a group.
In that group, there are 14 pipes across and they are stacked 9 pipes tall (from what I counted).
Knowing that, 14 * 9 can be broken down to 10 * 9 and 4 * 9.
10 * 9 is 90.
4 * 9 is 36.
Adding them together, there are 126 pipes in each set.
There are 2 stacks of 4 sets, so 8 total sets.
126 * 8 is 1008.
There are 1008 pipes on that truck.

My wife came up with a different way of doing it:

I counted all the way across and got 27 pipes.
I counted all the way up and got 36 pipes.
Hang on... (gets calculator)
There are 972 pipes.

So, which one of us is right? Neither? How did you do it?

Share your method and solution with me and I will feature it on the website! Here are a couple so far.

@Jstevens009 8 sections of about 15 by 10. So 150 times 8. Or 300 times 4. Or 600 times 2. 1200 pipes.

Table Talk Newsletter #33

Thank you to all who submitted number puzzles to share with others. I have taken a couple and compiled them here. As a thank you, I will be sending a signed copy of my upcoming book, Table Talk Math, to each of the families. My challenge to you is to try these out with your child and see if you can come up with the algebraic expression it is building.

Challenge 1, from Dylan (1st grade) in Wisconsin:

Pick any number

Add 10 to your number

Take away 3 from that number

Take away 8 from that number

Add 5 to that number

Subtract that number by your original number.

What did you get?

Dylan got 4, but how? What does the expression look like?

Thanks to Dylan and his dad, Thomas, for sharing. Make sure you email your conversation and result:john@tabletalkmath.com

Challenge 2, from Aleysa (6th grade) in Texas:

Pick any number

Multiply your number by 4

Multiply that number by 2

Subtract 6 from your number

Add 11 to your number

Add 3 to your number

Divide your number by 8

Subtract your original number from your new number

What did you get?

Aleysa got 1, but how? All that work for an answer of ONE?! What is the expression that her challenge created?

Thanks to Aleysa and her mom, Tatyannah, for sharing. Make sure you email your conversation and result:john@tabletalkmath.com

Next week, I will be showing you a picture that is sure to get the table talking. In the meantime, continue creating puzzles with your child and please share them with me. This has been fun to see the replies from all of you who have sent something in.

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.

Table Talk Newsletter #32

WARNING: April 1st is coming up quickly and I want to make sure you're ready. Nobody's going to pull a fast one on you, right?

So here's a challenge:

Pick any number

Add 5

Multiply that number by 4

Subtract 8 from that number

Divide that number by 4

Add 6 to that number

Subtract that number by your original number.

What did you get?

Did you get 9?

That was fun! But wait, how did I guess your number? What I did was build an algebraic expression, then I had you complete it, step by step.

For anyone looking at the problem first, it seems daunting. However, going step-by-step through the problem, it becomes more manageable. The end goal here is to make sure you end up with a last step like I did, such as:

x+9-x

That way, you know your original number will subtract to zero and you are left with a specific value. That is how I knew you ended with 9!

For younger kids, you might try something simpler:

Pick a number (not a zillion... something you can count to!)

Add 3 to your number

Add 2 to that number

Subtract your original number from your new number

You should have 5!

So here's my bigger challenge to you. Create one with your child, or with your class of students, and send it to me. I'm going to take a few of them and feature them on the website, tabletalkmath.com, and will be giving out a special prize to a few of my super-puzzlers. Challenge me!

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.

Table Talk Newsletter #31

There is a lot going on this week, so I want to make sure you had some ideas to try out with your child(ren) at home. Follow the links for more information or reach out to me and let me know what you wind up using!

When you and your child tries something from the site, please let me know; I would love to feature your products and your process. At the same time, Pi Day is about more than memorizing digits of pi. If you can get a string and measure circles, manipulate measurement, and understand the properties of why pi works, that's the real value.

March Madness

If you watch sports, there's a very good chance you know about March Madness, an annual test in your ability to pick the winning NCAA Basketball bracket. Can you do it without bias? Can you pick the upsets? Jordan Ellenburg, author of How Not to Be Wrong: The Power of Mathematical Thinking, offers up a mathematical approach to filling out your bracket that is worth checking out.

For the families with middle and high school students interested in college basketball, filling out a friendly bracket and seeing how your probability plays out is a fun and engaging way to use math to serve a conversation.

How is your bracket going? Let me know and I will feature it on an upcoming newsletter!

Lucky Leprechauns

Yes, St. Patrick's Day is right around the corner. With the majority of Google Searches littered with half-hearted attempts to engage children with math while they wear green, I was able to find one activity that is worth digging into: Lucky Leprechauns.

The focus of the game is for fifth graders, but you know your child and will know if it is interesting. As an 8th grade teacher, this is something I see being done in my classes, and might even try it out with my first grader... as long as I get to eat the candy afterwards.

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.

Table Talk Newsletter #30

Great news! For the Spanish version of this week's newsletter, click here, thanks to Ed Campos. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/ttm30spanish) with your Spanish-speaking friends.

This week's content is provided by Christina Tondevold, a mother who works with elementary math teachers and her own children to build math fluency in children. Her websites, both of which you need to explore:

This weekend, my family did our annual trip with two other families. One night we were playing a dice game and it was very interesting to see the difference in two of the little boys’ ability to recognize the amounts on the dice.

One of the boys is my 3 year-old son and he can quickly tell you all of the amounts on any side of the die. The other boy is actually 6 months older than my son and can tell you the amount when it was 1, but nothing else.

What I noticed during the game was these boys’ ability to subitize. Subitizing is the ability to recognize an amount without having to count. The interesting thing about subitizing is that you don’t get better at it just because you get older. Subitizing happens through the experiences you (or your child) has.

So, yes my child could subitize all the amounts on the die but it isn’t because he is ‘smarter’ or has that ‘math gene.’ It’s because he has had LOTS of experiences playing with dice. The more exposure he has had to the images on the dice, the quicker he is at identifying them and recognizing the amounts.

Games are such a powerful way to not only build subitizing in your children, but so many other math concepts. Our math abilities are developed through our experiences we have with mathematics. If children experience math through worksheets and tests they see math as boring (let’s be honest, how much fun are worksheets????). But if children experience math through games and puzzles and real-life problems they see math as interesting.

I’m a big fan of games because I grew up playing them and have wonderful memories of my family playing games, but also because they are easy for all of us parents to do at home. Here are my favorite math games:

Make 10 Go Fish

This game is played just like Go Fish but instead of matching cards, you want to make pairs that add up to ten. Deal 5 cards to each player. On each player’s turn they can lay down any “Ten Pairs” they have in their hand, then they ask any player for a number they need (example: I have an Ace so I ask another player if they have a nine). If that player has the nine they give it to the player who asked and the play continues to the next player. If not, the other player says “Go Fish” and the player draws one from the leftover deck of cards. Then it is the next player’s turn. Play ends when one player has gotten rid of all the cards in their hand.

Concentration

Layout 12 to 20 cards face down in rows & columns. This game is played just like Memory or Concentration, where you are trying to find matching cards. Player 1 flips over two cards, if those two cards match they get to keep those cards. If not, they turn them back over and play continues to the next person. Once Player 1 flips over two cards, it is the next player’s turn, even if Player 1 made a match. Make sure you are watching the other players so that you can concentrate on where the cards are for your turn.

You can adapt this to have ‘matches’ that total a certain amount. For example, if you have younger children you can use matches that add to 5. So, you would use all the 1 & 4 and 2 & 3 cards. If you wanted to make matches that add up to 10, you would need pairs of cards that add to 10.

Yahtzee

This classic game not only builds subitizing, but kids are also working on multiplication and addition and even probability. All you need are 5 dice and Yahtzee score cards which you can find here.

Combat/War

Two people take the entire deck of cards and deal them out face down between the two of them, so that each person has an equal amount in a pile. At the same time, each person flips over their top card. The person with the larger amount on their card gets to take both cards. If you flip over cards with the same amount, you each flip over another card to see who has the larger amount and then that player would take all the cards flipped over. Play continues until one player gets all the cards.

Make Your Own Game

Opportunities can come at anytime to turn something trivial into a powerful math building time, so keep your eyes open. One day my daughter had the set of Uno cards and she separated the deck and asked me what cards I thought she had showing. I asked her to give me a hint and she said “They make 11.” So I started guessing what combinations would make the 11 and eventually found the one she had. This then became a game we played over and over again and it was especially cool when I had the cards and gave her the hint. It was fun for me to see her process of how she thought about the combinations possible.

Building your child’s math mind can be done through the use of games. I love how fun it is for the kids and for me. They just see it as quality time with family, but I also see the underlying math that is being developed in them.

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.

Table Talk Newsletter #29

Great news! For the Spanish version of this week's newsletter, click here. Ed Campos has joined the team to provide a Spanish-translated version of our newsletters for parents who would appreciate it. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/TTM29spanish) with your Spanish-speaking friends.

Keep in mind that this is for the United States of America, so feel free to interchange it with wherever you and your family lives. For me and my family, this was an outstanding conversation using a globe and a little bit of creativity.

We talked about driving, which is what we normally do, and the amount of time it would take to travel all that distance. How far is it from our house to Florida? What about to Washington? Oh, how about ALASKA?! And we aren't even going to talk about Hawaii and how we would drive there...

So then we talked about flying, and how expensive it would be. After all, that's a flight for every single state, and that would get ridiculous in a hurry.

Because my kids are younger, we stopped with a lot of noticing and wondering and a little bit of counting and addition. I'm interested to hear where you might take this with your kids, so let me know!

XKCD took this question a step further and thought about how few straight lines it would take to touch all 50 states, assuming Alaska is Northwest of Washington and Hawaii is West-Southwest of California.

Table Talk Newsletter #28

Great news! For the Spanish version of this week's newsletter, click here. Ed Campos has joined the team to provide a Spanish-translated version of our newsletters for parents who would appreciate it. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/TTM27spanish) with your Spanish-speaking friends.

All you need for this week is:

string or clothesline

sheets of paper

a marker

two chairs

"Hey kids, I need your help putting these numbers in order. Do you think you could do it for me?"

On the table next to me is a stack of sheets of paper folded in half with a number on it, ready to be put onto the clothesline that is strung up between two dining room chairs.

Yes, this is a twist on the traditional number line activity and can be accessed by young children.

My boys spent around 5 minutes noticing, wondering, and exploring the number line by sliding sheets of paper across a string, spacing them out accordingly as more information became available. Because it was happening so fast, I wanted to throw a minor wrench in the system and did so with the 4 1/2. Even though he hadn't been introduced to fractions, it didn't take long to figure out that the 4 1/2 fell neatly between the 4 and the 5.

Next up, we are going to do sums:

1+5

3+6

2+4

...and so on

When they get older, we will head over to the clothesline math website and find more ideas and information to support both boys, but a clothesline will certainly be a part of our discussion for years to come.

Table Talk Newsletter #27

Great news! For the Spanish version of this week's newsletter, click here. Ed Campos has joined the team to provide a Spanish-translated version of our newsletters for parents who would appreciate it. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/TTM27spanish) with your Spanish-speaking friends.

Children interact with shape from a very early age and, to build on this, I encouraged my son (when he was about 2) to make patterns on the fridge from magnetic pattern blocks. As we continued experimenting together, we moved on to Polydron and, along the way, I became interested in using simple geometric animations to further engage my son, Dexter, (and then also my daughter, Cleo) in conversations about shapes and patterns in an attempt to engender an appreciation of the beauty of geometry. Often, at bedtime, my children would ask to see these ‘aminations’ as they sometimes called them when they were younger.

Many of the animations lend themselves to questions about how many shapes there are or the path taken by one particular shape, line or point. Some animations lead to more obvious questions. The one below, for example, simply morphs through a looping sequence of common polygons.

For example, by clicking on the image below, you'll see that the animation simply morphs through a looping sequence of common polygons.

The aim here is to encourage the identification of shapes while entertaining them with the way each shape morphs into the next. Can your child name each shape? What other questions can you ask about the animation?

Animations can also be a source of more complex questions. Click on the image below to see an example:

The answer to this question uses the concept of the lowest common multiple (or modulo arithmetic). However, there is a small sting in the tail. Did you get the right answer? There are also many other questions that we can ask:

How often do the triangle and square align? Why

How often do any two shapes align and why?

How does the answer change if a hexagon (with a dividing line) is added that takes 6s to rotate?

You can even encourage an empirical approach to the answer(s) and use a stopwatch!

There are around 100 animations on the Geometry Dad Twitter feed at the moment. In contrast, the Geometry Dad Facebook page generally contains photos of Dexter and Cleo’s constructions. These days, they mostly use Magnetic Polydron since it allows them to explore 2D and 3D space quickly and see their ideas come to life without being distracted by how the polygons attach to each other.

This is a great journey for me and my children. Feel free to join us!

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.

Table Talk Newsletter #25

Great news! For the Spanish version of this week's newsletter, click here. Ed Campos has joined the team to provide a Spanish-translated version of our newsletters for parents who would appreciate it. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/TTM26spanish) with your Spanish-speaking friends.

This week, my wife came home with a box of cards for our son to fill out and distribute to his first grade classmates. They're super cheesy and lack sincerity, but I guess that's what we've come down to.

As the kids get older, the distribution of cards becomes less and less until, at some point, they disappear altogether.

Well, thanks to Desmos, the free online graphing calculator that you really need to know about, you can now give out Math-O-Grams! Sure, you can use one of the pre-created templates and email it to a friend, but you can also create your own.

To create your own, head over to desmos.com/calculator and start designing. It would certainly help if your child is in high school, but it isn't necessary; here's one you can play with.

What can you create with mathematical functions that express your affection for a friend or loved one? I'd love to see what you come up with! Share your work by emailing them back to me, posting them onto Twitter, or sharing them on the Table Talk Math Facebook page.

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

A number of people mentioned that a Spanish version of the newsletter would benefit them or parents that they knew, so Ed has joined the team for that support. If you have any requests, please feel free to let me know.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.

Table Talk Newsletter #25

Great news! For the Spanish version of this week's newsletter, click here. Ed Campos has joined the team to provide a Spanish-translated version of our newsletters for parents who would appreciate it. Check it out and send Ed some love! Also, feel free to share the link (bit.ly/ttm25spanish) with your Spanish-speaking friends.

How many airplanes do you see in the image above?
How many terminals do you see?
How many people do you think this airport can serve in a day?
How much would all those airplanes cost?
Why did they design the airport terminals like this?

Sometimes, the best thing we can do to understand a problem is taking a step back and looking at it from a different approach. In The Daily Overview, you get a stunning satellite image of a new place around the world, all for free. In the image above, you are looking at Chicago O'Haire International Airport, an incredibly busy and large hub for travel, both domestic and international. Even better than asking these questions, find out what questions your child(ren) have after taking a minute or two to analyze it.

For more images like this, head over to www.dailyoverview.com/fiftyseven and explore the site. Maybe it isn't a math conversation that starts up, and that's completely fine. If we can give our children a different perspective, they might just begin taking a large-scale approach to other problems that they face as well.

So here's a way to report back: what questions did you and your family come up with? Did you find out any solutions to those questions? Share them by emailing them back to me, posting them onto Twitter, or sharing them on the Table Talk Math Facebook page.

If you have any questions, please feel free to contact me on Twitter (@TableTalkMath) or comment below. Be sure to have your friends sign up for the newsletter at tabletalkmath.com for weekly updates.

A number of people mentioned that a Spanish version of the newsletter would benefit them or parents that they knew, so Ed has joined the team for that support. If you have any requests, please feel free to let me know.

Thank you for taking the time to improve math fluency for children, one table talk conversation at a time.